Optimal Point-to-Point Trajectory Tracking of Redundant Manipulators using Generalized Pattern Search

Optimal point-to-point trajectory planning for planar redundant manipulator is considered in this study. The main objective is to minimize the sum of the position error of the end-effector at each intermediate point along the trajectory so that the end-effector can track the prescribed trajectory accurately. An algorithm combining Genetic Algorithm and Pattern Search as a Generalized Pattern Search GPS is introduced to design the optimal trajectory. To verify the proposed algorithm, simulations for a 3-D-O-F planar manipulator with different end-effector trajectories have been carried out. A comparison between the Genetic Algorithm and the Generalized Pattern Search shows that The GPS gives excellent tracking performance.Comment: www.ars-journal.co

Parallel algorithm and architecture for the control of kinematically redundant manipulators, A

Includes bibliographical references (pages 413-414).Kinematically redundant manipulators are inherently capable of more dexterous manipulation due to their additional degrees of freedom. To achieve this dexterity, however, one must be able to efficiently calculate the most desirable configuration from the infinite number of possible configurations that satisfy the end-effector constraint. It has been previously shown that the singular value decomposition (SVD) plays a crucial role in doing such calculations. In this work, a parallel algorithm for calculating the SVD is incorporated into a computational scheme for solving the equations of motion for kinematically redundant systems. This algorithm, which generalizes the damped least squares formulation to include solutions that utilize null-space projections and task prioritization as well as augmented or extended Jacobians, is then implemented on a simple linear array of processing elements. By taking advantage of the error bounds on the perturbation of the SVD, it is shown that an array of only four AT&T DSP chips can result in control cycle times of less than 3 ms for a seven degree-of-freedom manipulator

Modeling, Control, and Motion Analysis of a Class of Extensible Continuum Manipulators

In this dissertation, the development of a kinematic model, a configuration-space controller, a master-slave teleoperation controller, along with the analysis of the self-motion properties for redundant, extensible, continuous backbone (continuum) ``trunk and tentacle\u27 manipulators are detailed. Unlike conventional rigid-link robots, continuum manipulators are robots that can bend at any point along their backbone, resulting in new and unique modeling and control issues. Taken together, these chapters represent one of the first efforts towards devising model-based controllers of such robots, as well as characterizing their self-motion in its simplest form. Chapter 2 describes the development of a convenient set of generalized, spatial forward kinematics for extensible continuum manipulators based on the robot\u27s measurable variables. This development, takes advantage of the standard constant curvature assumption made for such manipulators and is simpler and more intuitive than the existing kinematic derivations which utilize a pseudo-rigid link manipulator. In Chapter 3, a new control strategy for continuum robots is presented. Control of this emerging new class of robots has proved difficult due to the inherent complexity of their dynamics. Using a recently established full Lagrangian dynamic model, a new nonlinear model-based control strategy (sliding-mode control) for continuum robots is introduced. Simulation results are illustrated using the dynamic model of a three-section, six Degree-of-Freedom, planar continuum robot and an experiment was conducted on the OctArm 9 Degree-of-Freedom continuum manipulator. In both the simulation and experiment, the results of the sliding-mode controller were found to be significantly better than a standard inverse-dynamics PD controller. In Chapter 4, the nature of continuum manipulator self-motion is studied. While use of the redundant continuum manipulator self-motion property (configuration changes which leave the end-effector location fixed) has been proposed, the nature of their null-spaces has not previously been explored. The manipulator related resolved-motion rate inverse kinematics which are based on the forward kinematics described in Chapter 2, are used. Based on these derivations, the self-motion of a 2-section, extensible redundant continuum manipulator in planar and spatial situations (generalizable to n-sections) is analyzed. The existence of a single self-motion manifold underlying the structures is proven, and simple self-motion cases spanning the null-space are introduced. The results of this analysis allow for a better understanding of general continuum robot self-motions and relate their underlying structure to real world examples and applications. The results are supported by experimental validation of the self-motion properties on the 9 Degree-of-Freedom OctArm continuum manipulator. In Chapter 5, teleoperation control of a kinematically redundant, continuum slave robot by a non-redundant, rigid-link master system is described. This problem is novel because the self-motion of the redundant robot can be utilized to achieve secondary control objectives while allowing the user to only control the tip of the slave system. To that end, feedback linearizing controllers are proposed for both the master and slave systems, whose effectiveness is demonstrated using numerical simulations and experimental results (using the 9 Degree-of-Freedom OctArm continuum manipulator as the slave system) for trajectory tracking as well as singularity avoidance subtask

Including a non-holonomic constraint in the FSP (full space parameterization) method for mobile manipulators` motion planning

The efficient utilization of the motion capabilities of mobile manipulators, i.e.. manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (d.o.f.) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a set of constraints such as obstacles in the workspace and various limits on the joint motions. A method, which we named the FSP (Full Space Parameterization), has recently been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. The application of the method to motion planning problems with obstacle and joint limit avoidance was discussed in some of our previous work. In this paper, we present the treatment in the FSP of a non-holonomic constraint on the platform motion, and give corresponding analytical solutions for resolving the redundancy with a general optimization criterion. Comparative trajectories involving a 10 d.o.f. mobile manipulator testbed moving with and without a non-holonomic constraint for the platform motion, are presented to illustrate the use and efficiency of the FSP approach in motion planning problems for highly kinematically redundant and constrained systems

Repeatable Motion Planning for Redundant Robots over Cyclic Tasks

We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method

Learning Utility Surfaces for Movement Selection

Humanoid robots are highly redundant systems with respect to the tasks they are asked to perform. This redundancy manifests itself in the number of degrees of freedom of the robot exceeding the dimensionality of the task. Traditionally this redundancy has been utilised through optimal control in the null-space. Some cost function is defined that encodes secondary movement goals and movements are optimised with respect to this functio

Task-space dynamic control of underwater robots

This thesis is concerned with the control aspects for underwater tasks performed by marine robots. The mathematical models of an underwater vehicle and an underwater vehicle with an onboard manipulator are discussed together with their associated properties. The task-space regulation problem for an underwater vehicle is addressed where the desired target is commonly specified as a point. A new control technique is proposed where the multiple targets are defined as sub-regions. A fuzzy technique is used to handle these multiple sub-region criteria effectively. Due to the unknown gravitational and buoyancy forces, an adaptive term is adopted in the proposed controller. An extension to a region boundary-based control law is then proposed for an underwater vehicle to illustrate the flexibility of the region reaching concept. In this novel controller, a desired target is defined as a boundary instead of a point or region. For a mapping of the uncertain restoring forces, a least-squares estimation algorithm and the inverse Jacobian matrix are utilised in the adaptive control law. To realise a new tracking control concept for a kinematically redundant robot, subregion tracking control schemes with a sub-tasks objective are developed for a UVMS. In this concept, the desired objective is specified as a moving sub-region instead of a trajectory. In addition, due to the system being kinematically redundant, the controller also enables the use of self-motion of the system to perform sub-tasks (drag minimisation, obstacle avoidance, manipulability and avoidance of mechanical joint limits)

Global motion planner for curve-tracing robots, A

Includes bibliographical references.We present a global motion planner for tracing curves in three dimensions with robot manipulator tool frames. This planner generates an efficient motion satisfying three types of constraints: constraints on the tool tip for curve tracing, robot kinematic constraints and robot link collision constraints. Motions are planned using a global search algorithm and a local planner based on a potential-field approach. This planner can be used with any robots including redundant manipulators, and can control the trade-offs between its algorithmic completeness and computation time. It can be applied in many robotic tasks such as seam welding, caulking, edge deburring and chamfering, and is expected to reduce motion programming times from days to minutes.This work has been performed at Sandia National Laboratories and supported by the U.S. Department of Energy under Contract DE-AC04-76DP00789

Increasing the Automation Level of Serial Robotic Manipulators with Optimal Design and Collision-free Path Control

The current hydraulic robotic manipulator mechanisms for heavy-duty machines are a mature technology, and their kinematics has been developed with a focus on the human operator maneuvering a hydraulically controlled system without numerical control input. As the trend in heavy-duty manipulators is increased automation, computer control systems are increasingly being widely used, and the requirements for robotic manipulator kinematics are different. Computer control enables a different kind of robotic manipulator kinematics, which is not optimum for direct control by a human operator, because the joint motions related to the different trajectories are not native for the human mind. Numerically controlled robotic manipulators can accept kinematics that is more efficient at doing the job expected by the customer.To increase the autonomous level of robotic manipulator, the optimal structure is not enough, but it is a part of the solution toward a fully autonomous manipulator. The control system of the manipulator is the main part of computer-controlled manipulators. A collision avoidance system plays an important role in the field of autonomous robotics. Without collision avoidance functionality, it is quite obvious that only very simple movements and tasks can be carried out automatically. With more complicated movement and manipulators, some kind of collision avoidance system is required. An unknown or changing environment increases the need for an intelligent collision avoidance system that can find a collision-free path in a dynamic environment.This thesis deals with these fundamental challenges by optimizing the serial manipulator structure for the desired task and proposing a collision avoidance control system. The basic requirement in the design of such a robotic manipulator is to make sure that all the desired task points can be achieved without singularities. These properties are difficult to achieve with the general shape and type of robotic manipulators. In this research work, a task-based kinematic synthesis approach with the proper optimization method ensures that the desired requirements can be fulfilled.To enable autonomous task execution for robotic manipulators, the control systems must have a collision avoidance system that can prevent different kinds of collisions. These collisions include self-collisions, collisions with other manipulators, collisions with obstacles, and collisions with the environment. Furthermore, there can be multiple simultaneous possible collisions that need to prevented, and the collision system must be able to handle all these collisions in real-time. In this research work, a real-time collision avoidance control approach is proposed to handle these issues. Overall, both topics, covered in this thesis, are believed to be key elements for increasing the automation of serial robotic manipulators